New Perspective on the Optical Theorem of Classical Electrodynamics

A general proof of the optical theorem (also known as the optical cross-section theorem) is presented that reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave within the scatterer. The oscillating electric charges and currents as well as the electric and magnetic dipoles of the scatterer, driven by an incident plane-wave, extract energy from the incident beam at a certain rate. The same oscillators radiate electro-magnetic energy into the far field, thus giving rise to well-defined scattering amplitudes along various directions. The essence of the proof presented here is that the extinction cross-section of an object can be related to its forward scattering amplitude using the induced oscillations within the object but without an actual knowledge of the mathematical form assumed by these oscillations.Comment: 7 pages, 1 figure, 12 reference

Effect of microsegregation and heat treatment on localised γ and γ’ compositions in single crystal Ni-based superalloys

The present work investigates the impact of residual segregation on the underlying microstructure of a 3rd generation single crystal, nickel-based superalloy to understand potential variation in mechanical behaviour between dendrite cores and interdendritic regions. Despite the applied heat-treatments, chemical variation between dendrite cores and interdendritic regions persisted particularly for elements Re, Nb and Ta. Atom probe tomography (APT) was utilized for its nanoscale capability to map site-specific chemical changes in the γ matrix, γ’ precipitates and across the γ/γ’ interface. Greater interfacial segregation of Re, matched by a corresponding depletion of Ni were observed within dendrite cores, with the extent found to increase following heat treatment. Differences in lattice parameters between dendrite cores and interdendritic regions were identified, with larger lattice misfits associated with interdendritic regions

A Forward-Design Approach to Increase the Production of Poly-3-Hydroxybutyrate in Genetically Engineered Escherichia coli

Biopolymers, such as poly-3-hydroxybutyrate (P(3HB)) are produced as a carbon store in an array of organisms and exhibit characteristics which are similar to oil-derived plastics, yet have the added advantages of biodegradability and biocompatibility. Despite these advantages, P(3HB) production is currently more expensive than the production of oil-derived plastics, and therefore, more efficient P(3HB) production processes would be desirable. In this study, we describe the model-guided design and experimental validation of several engineered P(3HB) producing operons. In particular, we describe the characterization of a hybrid phaCAB operon that consists of a dual promoter (native and J23104) and RBS (native and B0034) design. P(3HB) production at 24 h was around six-fold higher in hybrid phaCAB engineered Escherichia coli in comparison to E. coli engineered with the native phaCAB operon from Ralstonia eutropha H16. Additionally, we describe the utilization of non-recyclable waste as a low-cost carbon source for the production of P(3HB)

Selective function of the PDZ domain of Dishevelled in noncanonical Wnt signalling

Dishevelled is a cytoplasmic hub that transduces Wnt signals to cytoplasmic effectors, which can be broadly characterised as canonical (β-catenin dependent) and noncanonical, to specify cell fates and behaviours during development. To transduce canonical Wnt signals, Dishevelled binds to the intracellular face of Frizzled through its DEP domain and polymerises through its DIX domain to assemble dynamic signalosomes. Dishevelled also contains a PDZ domain, whose function remains controversial. Here, we use genome editing to delete the PDZ domain-encoding region from Drosophila dishevelled. Canonical Wingless signalling is entirely normal in these deletion mutants; however, they show defects in multiple contexts controlled by noncanonical Wnt signalling, such as planar polarity. We use nuclear magnetic resonance spectroscopy to identify bona fide PDZ-binding motifs at the C termini of different polarity proteins. Although deletions of these motifs proved aphenotypic in adults, we detected changes in the proximodistal distribution of the polarity protein Flamingo (also known as Starry night) in pupal wings that suggest a modulatory role of these motifs in polarity signalling. We also provide new genetic evidence that planar polarity relies on the DEP-dependent recruitment of Dishevelled to the plasma membrane by Frizzled

Planar cell polarity: the Dachsous/Fat system contributes differently to the embryonic and larval stages of Drosophila.

The epidermal patterns of all three larval instars (L1-L3) ofDrosophilaare made by one unchanging set of cells. The seven rows of cuticular denticles of all larval stages are consistently planar polarised, some pointing forwards, others backwards. In L1 all the predenticles originate at the back of the cells but, in L2 and L3, they form at the front or the back of the cell depending on the polarity of the forthcoming denticles. We find that, to polarise all rows, the Dachsous/Fat system is differentially utilised; in L1 it is active in the placement of the actin-based predenticles but is not crucial for the final orientation of the cuticular denticles, in L2 and L3 it is needed for placement and polarity. We find Four-jointed to be strongly expressed in the tendon cells and show how this might explain the orientation of all seven rows. Unexpectedly, we find that L3 that lack Dachsous differ from larvae lacking Fat and we present evidence that this is due to differently mislocalised Dachs. We make some progress in understanding how Dachs contributes to phenotypes of wildtype and mutant larvae and adults.This work was generously supported by the Wellcome Trust: a Project Grant [086986] and, later, two successive Investigator Awards, [096645 and 107060] awarded to P.A.L., as well as [100986] to D.S. P.S. thanks Fundaçã o para a Ciência e a Tecnologia and the Cambridge Philosophical Society for research studentships.This is the final version of the article. It first appeared from The Company of Biologists via https://doi.org/10.1242/bio.01715

Scattering of electromagnetic waves by many small perfectly conducting or impedance bodies

A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape, an explicit analytical formula is derived for the scattering amplitude. The formula holds as a → 0, where a is a characteristic size of the small particle and the wavelength is arbitrary but fixed. The scattering amplitude for a small impedance particle is shown to be proportional to a2−κ, where κ ∈ [0,1) is a parameter which can be chosen by an experimenter as he/she wants. The boundary impedance of a small particle is assumed to be of the form ζ = ha−κ, where h = const, Reh ≥ 0. The scattering amplitude for a small perfectly conducting particle is proportional to a3, and it is much smaller than that for the small impedance particle. The many-body scattering problem is solved under the physical assumptions a ≪ d ≪ λ, where d is the minimal distance between neighboring particles and λ is the wavelength. The distribution law for the small impedance particles is N(∆) ∼ 1/a2−κ∆ N(x)dx as a → 0. Here, N(x) ≥ 0 is an arbitrary continuous function that can be chosen by the experimenter and N(∆) is the number of particles in an arbitrary sub-domain ∆. It is proved that the EM field in the medium where many small particles, impedance or perfectly conducting, are distributed, has a limit, as a → 0 and a differential equation is derived for the limiting field. On this basis, a recipe is given for creating materials with a desired refraction coefficient by embedding many small impedance particles into a given material. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929965

Specific "scientific" data structures, and their processing

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while elaborating some theory and its consequences, are rather: power series and Pad\'e approximants, differential forms and other instances of differential algebras, functionals (for the variational calculus), trajectories (solutions of differential equations), Young diagrams and Feynman graphs, etc. Such data is often used in a [semi-]numerical setting, not necessarily "symbolic", appropriate for the computer algebra packages. Modules adapted to such data may be "just libraries", but often they become specific, embedded sub-languages, typically mapped into object-oriented frameworks, with overloaded mathematical operations. Here we present a functional approach to this philosophy. We show how the usage of Haskell datatypes and - fundamental for our tutorial - the application of lazy evaluation makes it possible to operate upon such data (in particular: the "infinite" sequences) in a natural and comfortable manner.Comment: In Proceedings DSL 2011, arXiv:1109.032

Rapid disruption of dishevelled activity uncovers an intercellular role in maintenance of prickle in core planar polarity protein complexes

Planar polarity, the coordinated polarization of cells in the plane of a tissue, is important for normal tissue development and function. Proteins of the core planar polarity pathway become asymmetrically localized at the junctions between cells to form intercellular complexes that coordinate planar polarity between cell neighbors. Here, we combine tools to rapidly disrupt the activity of the core planar polarity protein Dishevelled, with quantitative measurements of protein dynamics and levels, and mosaic analysis, to investigate Dishevelled function in maintenance of planar polarity. We provide mechanistic insight into the hierarchical relationship of Dishevelled with other members of the core planar polarity complex. Notably, we show that removal of Dishevelled in one cell causes rapid release of Prickle into the cytoplasm in the neighboring cell. This release of Prickle generates a self-propagating wave of planar polarity complex destabilization across the tissue. Thus, Dishevelled actively maintains complex integrity across intercellular junctions

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.Comment: 4 pages, REVTe

New Insights into the Generation of CD4 Memory May Shape Future Vaccine Strategies for Influenza

Influenza viral evolution presents a formidable challenge to vaccination due to the virus\u27 ability to rapidly mutate to evade immune responses. Live influenza infections generate large and diverse CD4 effector T cell responses that yield highly protective, long-lasting CD4 T cell memory that can target conserved viral epitopes. We review advances in our understanding of mechanisms involved in generating CD4 T cell responses against the influenza A virus (IAV), focusing on specialized follicular helper (TFH) and CD4 cytotoxic (ThCTL) effector subsets and on CD4 T cell memory. We also discuss two recent findings in context of enhancing vaccine responses. First, helper T cells require priming with APC secreting high levels of IL-6. Second, the transition of IAV-generated effectors to memory depends on IL-2, costimulation and antigen signals, just before effectors reach peak numbers, defined as the memory checkpoint. The need for these signals during the checkpoint could explain why many current influenza vaccines are poorly effective and elicit poor cellular immunity. We suggest that CD4 memory generation can be enhanced by re-vaccinating at this time. Our best hope lies in a universal vaccine that will not need to be formulated yearly against seasonal antigenically novel influenza strains and will also be protective against a pandemic strain. We suggest a vaccine approach that elicits a powerful T cell response, by initially inducing high levels of APC activation and later providing antigen at the memory checkpoint, may take us a step closer to such a universal influenza vaccine